It goes like this: the fourth, the fifth, the minor chord, the major lift. By the end of this Christmas season, you will doubtless be familiar with the rise and fall of Leonard Cohen's Hallelujah; you will have heard it spilling out of radio speakers, crooned by X-Factor winners and indie heartthrobs. You will be aware of how, in one great ribbon of C major, he bound together music, religion and mankind, King David, Bathsheba and kitchen chairs.

Its composition famously reduced Cohen to sitting in his underwear on the carpeted floor of his room at the Royalton Hotel in New York, filling notebooks, banging his head against the floor. "To find that song, that urgent song, takes a lot of versions and a lot of work and a lot of sweat," he told Paul Zollo in an interview for SongTalk magazine. There were some 80 verses drafted for Hallelujah, and later there would be another version still, somewhat bleaker in its conclusion: "Maybe there's a God above/ But all I ever learned from love/ Was how to shoot at someone who outdrew ya/ It's not a cry that you hear at night/ It's not somebody who's seen the light/ It's a cold and it's a broken hallelujah."

It was always the John Cale version that did it for me; his voice seemed to bring a more ecclesiastical quality to those lines. For a long while I clung to that and resisted the prettiness of Jeff Buckley's version, but Buckley's is undoubtedly the most sensual interpretation, breathing life into the song with a short exhalation even before he plays, bringing out the texture of Cohen's lyrics, the feel of lips and hair and coldness. He takes its holiness and renders it physical, earthly. "Whoever listens closely to Hallelujah will discover that it is a song about sex, about love, about life on earth," Buckley once explained. "The hallelujah is not a homage to a worshipped person, idol or god, but the hallelujah of the orgasm. It's an ode to life and love." After all, what is a minor fall if not a petite mort?

Hallelujah appeared on Various Positions, an album that prompted Dylan to note that Cohen's songs were becoming more like prayers. In fact, a few songs along on the track listing, you'll find If It Be Your Will, a kind of prayer-like companion to Hallelujah: "If it be your will/ that a voice be true,/ from this broken hill/ I will sing to you./ From this broken hill/ all your praises they shall ring/ if it be your will/ to let me sing ..."

Dylan covered Hallelujah, too, but he chose the first version, the one that ended with the chirrup of: "And even though/ It all went wrong/ I'll stand before the Lord of Song/ With nothing on my tongue but hallelujah." He chose a kind of defiance over a defeat. But it is the brokenness of the later version of Hallelujah that has always seemed to me the song's most essential quality.

Because brokenness has always been a constant in the work of Cohen - the broken Jesus of Suzanne, the fallen robin of Chelsea Hotel No 2, the broken hill of If It Be Your Will, the cold and broken hallelujah. And this brokenness brings to his lyrics not only the pain and disappointment of being a flawed human being, and the perpetual effort to be better, but also the sensual quality of being mere flesh and bone.

Some years later, Cohen was discussing with Zollo the song Anthem from his 1992 album The Future, a song that begins with birds singing at the break of day, encouraging us to "start again". Zollo asks him about a line from its chorus: "Forget your perfect offering/ There is a crack in everything/ That's how the light gets in." To which Cohen replies: "That has been the background of much of my work ... All human activity is flawed ... it is by intimacy with the flaw that we discern our real humanity and our real connection with divine inspiration." And it is in that redrafted version of Hallelujah, where he ends loveless, maybe Godless, cracked and cold and broken, that the light truly gets in.